Question

Find the area of the triangle PQR

i. If the base QR=16cm and the height PS is 4 cm.
ii. Find the height QM, if PR =8 cm.

Answer 1

Step-by-step explanation:

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Class 7

>>Maths

>>Perimeter and Area

>>Area of a Triangle

>>In Fig, if PR = 12 cm, QR = 6 cm and PL

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In Fig, if PR=12cm,QR=6cm and PL=8cm, then QM is

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Solution

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Correct option is C)

Given that PL=8cm

PR=12cm

QR=6cm

Now, in right-angled triangle PLR

Using Pythagoras theorem,

⇒PR

2

=PL

2

+LR

2

⇒LR

2

=144−64

=

80

=4

5

cm

LR=LQ+QR

⇒LQ=LR−QR=(4

5

−6) cm

Now area of triangle PLR

A=

2

1

×(4

5

)×8

=16

5

cm

2

Now, area of triangle PLQ

A=

2

1

×(4

5

−6)×8

=(16

5

−24)cm

2

Hence, area of triangle PLR = Area of triangle PLQ + Area of triangle PQR

So, area of triangle PLR − Area of triangle PLQ = Area of triangle PQR

⇒16

5

−(16

5

−24),

⇒ Area of triangle PQR =24cm

2

⇒

2

1

×PR×QM=24

⇒

2

1

×12×QM=24

∴QM=4cm